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Testing and relaxing the exclusion restriction in the control function approach

控制函数方法中排除限制的检验与放松

The control function approach which employs an instrumental variable excluded from the outcome equation is a very common solution to deal with the problem of endogeneity in nonseparable models. Exclusion restrictions, however, are frequently controversial. We first argue that, in a nonparametric triangular structure typical of the control function literature, one can actually test this exclusion restriction provided the instrument satisfies a local irrelevance condition.…

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Two-way fixed effects and differences-in-differences estimators with several treatments

多种处理下的双向固定效应与双重差分估计

We study two-way-fixed-effects regressions (TWFE) with several treatment variables. Under a parallel trends assumption, we show that the coefficient on each treatment identifies a weighted sum of that treatment’s effect, with possibly negative weights, plus a weighted sum of the effects of the other treatments. Thus, those estimators are not robust to heterogeneous effects and may be contaminated by other treatments’ effects. We further show that omitting a treatment from…

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Nonparametric difference-in-differences in repeated cross-sections with continuous treatments

重复截面与连续处理下的非参数双重差分

This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an exogenous change over time which affects the treatment in a heterogeneous way, stationarity of the distribution of unobservables and a rank invariance condition on the time trend. On the other hand, we do not impose any functional form…

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Empirical process results for exchangeable arrays

可交换数组的经验过程结果

Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same population. Examples include trade flows between countries or relationships in a network. Separately exchangeable arrays are well suited to multiway clustering, where units sharing the same cluster (e.g., geographical areas or sectors of activity…

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A Cautionary Tale on Instrumental Calibration for the Treatment of Nonignorable Unit Nonresponse in Surveys

调查中不可忽略单位无应答的工具校准:一则警示

Response rates have been steadily declining over the last decades, making survey estimates vulnerable to nonresponse bias. To reduce the potential bias, two weighting approaches are commonly used in National Statistical Offices: the one-step and the two-step approaches. In this article, we focus on the one-step approach, whereby the design weights are modified in a single step with two simultaneous goals in mind: reduce the nonresponse bias and ensure the consistency between…

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Extremal quantile regressions for selection models and the black–white wage gap

样本选择模型的极端分位数回归与黑人—白人工资差距

We consider the estimation of a semiparametric sample selection model without instrument or large support regressor. Identification relies on the independence between the covariates and selection, for arbitrarily large values of the outcome. We propose a simple estimator based on extremal quantile regression and establish its asymptotic normality by extending previous results on extremal quantile regressions to allow for selection. Finally, we apply our method to estimate…

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Identification of additive and polynomial models of mismeasured regressors without instruments

无工具变量下误测解释变量的可加与多项式模型识别

We show nonparametric point identification of a measurement error model with covariates that can be interpreted as invalid instruments. Our main contribution is to replace standard exclusion restrictions with the weaker assumption of additivity in the covariates. Measurement errors are ubiquitous and additive models are popular, so our results combining the two should have widespread potential application. We also identify a model that replaces the nonparametric function of…

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Identification of mixture models using support variations

利用支持集变化识别混合模型

We consider the issue of identifying nonparametrically continuous mixture models. In these models, all observed variables depend on a common and unobserved component, but are mutually independent conditional on it. Such a structure applies for instance to measurement error, matching and auction models. Traditional approaches rely on parametric assumptions or strong functional restrictions. We show that these models are actually identified nonparametrically if the supports of…

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Inference on an extended Roy model, with an application to schooling decisions in France

扩展 Roy 模型的推断及其在法国教育选择中的应用

This paper considers the identification and estimation of an extension of Roy’s model (1951) of sectoral choice, which includes a non-pecuniary component in the selection equation and allows for uncertainty on potential earnings. We focus on the identification of the non-pecuniary component, which is key to disentangling the relative importance of monetary incentives versus preferences in the context of sorting across sectors. By making the most of the structure of the…

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